hyperelliptic(.ncag).info

holonomy group

$\mathrm{S}_3 \times \mathrm{C}_{12}$, order $72$, SmallGroup $[72,27]$ · character table

tangent representation $\rho$

$\rho(g_{1}) = \operatorname{diag}(1, 1, -1, -1)$

$\rho(g_{2}) = \operatorname{diag}(1, i, -1, -1)$

$\rho(g_{3}) = \operatorname{diag}(1, 1, \zeta_{3}, \zeta_{3})$

$\rho(g_{4}) = \operatorname{diag}(1, 1, 1, -1)$

$\rho(g_{5}) = \operatorname{diag}(1, 1, \zeta_{3}, \zeta_{3}^{2})$

$\rho \cong$ $\chi_{ 1 }$ $\oplus$ $\chi_{ 7 }$ $\oplus$ $\chi_{ 28 }$

order of $\omega_X$

12

number of moduli

1

irregularity $q = \dim \operatorname{Aut}^0(X)$

1

Albanese

the Albanese variety has dimension $1$; the general fiber has dimension $3$ and is an abelian variety or a hyperelliptic variety (details)

$\mathbf{D}^{\mathrm{b}}(X)$

indecomposability open (why)

Hochschild cohomology $\dim \mathrm{HH}^\bullet$

$(1, 2, 1, 0, 0, 0, 0, 0, 0)$

Hodge diamond

polyvector fields $\mathrm{H}^q(X,\bigwedge^p T_X)$